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Find the slope of the tangent to the curve

y = 3x^2 - 2x + 1

x = 1

Jun 11, 2024

Find the slope of the tangent to the curve

y = 3x^2 - 2x + 1

x = 1

Generated Graph

Solution by Steps

step 1

To find the slope of the tangent line to the curve

y = 3x^2 - 2x + 1

x = 1

, we first need to find the derivative of the function

step 2

The derivative of

y = 3x^2 - 2x + 1

y' = \frac{d}{dx}(3x^2 - 2x + 1)

step 3

Using the power rule, the derivative is

y' = 6x - 2

step 4

Now, we evaluate the derivative at

x = 1

y'(1) = 6(1) - 2 = 6 - 2 = 4

step 5

Therefore, the slope of the tangent line to the curve at

x = 1

4

Answer

The slope of the tangent line to the curve

y = 3x^2 - 2x + 1

x = 1

4

Key Concept

Derivative

Explanation

The derivative of a function at a given point provides the slope of the tangent line to the curve at that point.